Question

the ratio of the diffusion rates of two gases is given by the formula r1/r2=square root m2/square root m1 wherem1 and m2 are the masses of the molecules of the gases. find r1/r2 if m1=12 units and m2=30 units. your answer should be in simplified radical form

Answer 1

The simplified radical form is given as:

`(r_1)/(r_2)=\sqrt{(5)/(2)}`

Explanation:

It is given that:

the ratio of the diffusion rates of two gases is given by the formula:

`(r_1)/(r_2)=(√(m_2))/(√(m_1))`

where
`m_1\ and\ m_2` are the masses of the molecules of the two gases.

Now we are given:

`m_1=12\ units\ \text{and}\ m_2=30\ units.`

Hence,

`(r_1)/(r_2)=(√(30))/(√(12))\\\\\\(r_1)/(r_2)=(√(30))/(2√(3))\\\\(r_1)/(r_2)=(√(2)\cdot √(3)\cdot √(5))/(2√(3))\\\\(r_1)/(r_2)=(√(2)\cdot √(5))/(2)`

`(r_1)/(r_2)=(√(5))/(√(2))`

Hence, the simplified radical form is:

`(r_1)/(r_2)=\sqrt{(5)/(2)}`

Answer 2

The value of
`(r1)/(r2)` is
`\sqrt{} (5)/(2)`

The given diffusion rate equation is:


`(r1)/(r2) = \sqrt{} (m2)/(m1)`

Now,


`(r1)/(r2) = \sqrt{} (30)/(12)`

Breaking 30 and 12 into its factors

= \sqrt{} \frac{2×3×5}{2×2×3} [/tex]

= \sqrt{} \frac{5}{2} [/tex]